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Sherali-Adams and the binary encoding of combinatorial principles.

Dantchev, Stefan and Ghani, Abdul and Martin, Barnaby (2020) 'Sherali-Adams and the binary encoding of combinatorial principles.', in LATIN 2020: Theoretical Informatics. , pp. 336-347. Lecture Notes in Computer Science., 12118

Abstract

We consider the Sherali-Adams ( SA ) refutation system together with the unusual binary encoding of certain combinatorial principles. For the unary encoding of the Pigeonhole Principle and the Least Number Principle, it is known that linear rank is required for refutations in SA , although both admit refutations of polynomial size. We prove that the binary encoding of the Pigeonhole Principle requires exponentially-sized SA refutations, whereas the binary encoding of the Least Number Principle admits logarithmic rank, polynomially-sized SA refutations. We continue by considering a refutation system between SA and Lasserre (Sum-of-Squares). In this system, the unary encoding of the Least Number Principle requires linear rank while the unary encoding of the Pigeonhole Principle becomes constant rank.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/978-3-030-61792-9_27
Publisher statement:The final authenticated version is available online at https://doi.org/10.1007/978-3-030-61792-9_27
Date accepted:10 February 2020
Date deposited:30 June 2020
Date of first online publication:03 December 2020
Date first made open access:21 June 2021

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